
NAMEzunmbr.f SYNOPSISFunctions/Subroutinessubroutine zunmbr (VECT, SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, WORK, LWORK, INFO) Function/Subroutine Documentationsubroutine zunmbr (characterVECT, characterSIDE, characterTRANS, integerM, integerN, integerK, complex*16, dimension( lda, * )A, integerLDA, complex*16, dimension( * )TAU, complex*16, dimension( ldc, * )C, integerLDC, complex*16, dimension( * )WORK, integerLWORK, integerINFO)ZUNMBR Purpose:If VECT = 'Q', ZUNMBR overwrites the general complex MbyN matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N': Q * C C * Q TRANS = 'C': Q**H * C C * Q**H If VECT = 'P', ZUNMBR overwrites the general complex MbyN matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N': P * C C * P TRANS = 'C': P**H * C C * P**H Here Q and P**H are the unitary matrices determined by ZGEBRD when reducing a complex matrix A to bidiagonal form: A = Q * B * P**H. Q and P**H are defined as products of elementary reflectors H(i) and G(i) respectively. Let nq = m if SIDE = 'L' and nq = n if SIDE = 'R'. Thus nq is the order of the unitary matrix Q or P**H that is applied. If VECT = 'Q', A is assumed to have been an NQbyK matrix: if nq >= k, Q = H(1) H(2) . . . H(k); if nq < k, Q = H(1) H(2) . . . H(nq1). If VECT = 'P', A is assumed to have been a KbyNQ matrix: if k < nq, P = G(1) G(2) . . . G(k); if k >= nq, P = G(1) G(2) . . . G(nq1). VECT
Author:
VECT is CHARACTER*1 = 'Q': apply Q or Q**H; = 'P': apply P or P**H.SIDE SIDE is CHARACTER*1 = 'L': apply Q, Q**H, P or P**H from the Left; = 'R': apply Q, Q**H, P or P**H from the Right.TRANS TRANS is CHARACTER*1 = 'N': No transpose, apply Q or P; = 'C': Conjugate transpose, apply Q**H or P**H.M M is INTEGER The number of rows of the matrix C. M >= 0.N N is INTEGER The number of columns of the matrix C. N >= 0.K K is INTEGER If VECT = 'Q', the number of columns in the original matrix reduced by ZGEBRD. If VECT = 'P', the number of rows in the original matrix reduced by ZGEBRD. K >= 0.A A is COMPLEX*16 array, dimension (LDA,min(nq,K)) if VECT = 'Q' (LDA,nq) if VECT = 'P' The vectors which define the elementary reflectors H(i) and G(i), whose products determine the matrices Q and P, as returned by ZGEBRD.LDA LDA is INTEGER The leading dimension of the array A. If VECT = 'Q', LDA >= max(1,nq); if VECT = 'P', LDA >= max(1,min(nq,K)).TAU TAU is COMPLEX*16 array, dimension (min(nq,K)) TAU(i) must contain the scalar factor of the elementary reflector H(i) or G(i) which determines Q or P, as returned by ZGEBRD in the array argument TAUQ or TAUP.C C is COMPLEX*16 array, dimension (LDC,N) On entry, the MbyN matrix C. On exit, C is overwritten by Q*C or Q**H*C or C*Q**H or C*Q or P*C or P**H*C or C*P or C*P**H.LDC LDC is INTEGER The leading dimension of the array C. LDC >= max(1,M).WORK WORK is COMPLEX*16 array, dimension (MAX(1,LWORK)) On exit, if INFO = 0, WORK(1) returns the optimal LWORK.LWORK LWORK is INTEGER The dimension of the array WORK. If SIDE = 'L', LWORK >= max(1,N); if SIDE = 'R', LWORK >= max(1,M); if N = 0 or M = 0, LWORK >= 1. For optimum performance LWORK >= max(1,N*NB) if SIDE = 'L', and LWORK >= max(1,M*NB) if SIDE = 'R', where NB is the optimal blocksize. (NB = 0 if M = 0 or N = 0.) If LWORK = 1, then a workspace query is assumed; the routine only calculates the optimal size of the WORK array, returns this value as the first entry of the WORK array, and no error message related to LWORK is issued by XERBLA.INFO INFO is INTEGER = 0: successful exit < 0: if INFO = i, the ith argument had an illegal value Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
November 2011
Definition at line 196 of file zunmbr.f.
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